1. Field of the Invention
The present invention relates to a scanning electron microscope having a plurality of detectors and particularly to a scanning electron microscope providing an operation unit for computing surface topography from a two dimensional normal distribution and a method of processing the same.
2. Description of the Prior Art
The method for obtaining a topography of a specimen surface from the two dimensional distribution of a normal vector is now used as the method to obtain a cubic topography by picking up a plurality of images in different positions of a light source. The method obtains the direction of a normal vector without changing the relationship between a point of view and a specimen (called Photometric Stereo method, PMS). Another method to compute a topography is by providing a plurality of detectors to a scanning electron microscope (hereinafter abbreviated as SEM) based on the same principle and by obtaining the normals using images formed from the signals of the detectors (called SEM-PMS method). For example, the Computer Graphics and Image Processing Vol. 18, pp. 309-328 (1982)) employs the following method (notation is changed). The normal vector n(x,y)=(-p(x,y), -q(x,y),1) is obtained on the lattice points of -i.sub.0 .ltoreq.x.ltoreq.i.sub.0, -j.sub.0 .ltoreq.y.ltoreq.j.sub.0. However, when the formula of the surface to obtain a topography is expressed by z=f(x, y) with the z axis indicating the height direction, p=.differential.f/.differential.x, q=.differential.f/.differential.y. From the two dimensional distribution of of normal vector, the surface topography is obtained in the following procedures (hereinafter, normal distribution is integrated or successively added (hereinafter called integration and the equivalent operation)).
(1) A desired height z.sub.0 is given to the origin. EQU z(0,0)=z.sub.0
(2) Integration and the equivalent operation is carried out for x and y axes from the origin. ##EQU1## (3) Heights of quadrants are externally integrated. (3-1) First quadrant:
z(i,j) is obtained by the following formula when z(i-1,j) and z(i,j-1) are already obtained. ##EQU2##
This formula corresponds to a mean value of the height obtained from z(i-1, j) using the differential coefficient of x or approximated differential coefficient (hereinafter referred to as differential coefficient and the equivalent) and the height obtained from z(i, j-1) using the differential coefficient and the equivalent.
(3-2) Second quadrant:
z(i,j) is obtained from z(i+1,j), z(i,j-1). ##EQU3## (3-3) Third quadrant:
z(i,j) is obtained from z(i+1,j), z(i,j+1). ##EQU4## (3-4) Fourth quadrant:
z(i,j) is obtained from z(i-1,j), z(i,j+1). ##EQU5##
The method indicated in the reference conducts successively and externally the integration and the equivalent operation from the origin. In case an error is not included in the normal distribution, accurate surface topography can be obtained by the integrations in any procedures. However, in many cases, the normal distribution is a measured value and includes an error. The method of the reference provides a problem that an error is accummulated with the proceeding of the external integration and a large distortion is generated at the peripheral area.
FIG. 9(a) is a contour display as a result of the application of the prior art method to the pyramid-like recessed area, wherein large distortions are generated at the four corners (particularly, upper left and lower right points).
Japanese Patent Laid-open No. 62-6112 is related to the above-described method.
The prior art suffers from a problem that errors give large distortions to the results of integrations when errors are included in the normal distribution.